and some pliers, although the fasteners are soft enough you could probably do it by hand

I had tried using a kumihimo disc already, and I knew I didn't want slots, but help keeping the strands separate meant a shape with concave sides like so:
The hole was for the finished braid to pass through. Lastly I wanted somewhere to park the pass through loop, somewhere above the plane of the tool. So, I got some fasteners and made this shape:
and pushed it through the foam.

The finished thing looks like this:

Ergonomically, holding the tool was definitely easier than holding just the braid.

Did the star shape help with fumbling around for the strands? I think it did.

Did the pass through loop parking prong do the trick? If you were using cord, I think it would have been a waste of time since there was still some fumbling involved with the prong. Using thread as I was for stringing the beads, it was definitely better than nothing.

Were I to work on refining the foam tool, I would extend two of the star arms, and maybe carve a channel into them to hold the parked loop to make a bigger target, using bigger gestures. Using the loop parking prong as above was still more fiddly than I would like.